An automorphism of a group G is called regular if it moves every element of G except the identity. BURNSIDE proved that a finite group G has a regular automorphism of order two if and only if G is an abelian group of odd order, and then the only such automorphism maps every element onto its inverse ([21, p. 230). More recently several authors considered the question: what groups can admit regul...

Introduction: Oxidative stress is an important factor in the induction of diabetes complications especially peripheral neuropathy and hyperalgesia, and it has been proven that regular aerobic exercise and vitamin E have antioxidant effects. Therefore, this study was designed to examine effects of regular aerobic exercise and vitamin E on thermal pain threshold in streptozocin-induced diabeti...

This paper addresses the question of determining, for a given graph G, all regular maps having G as their underlying graph, i.e., all embeddings of G in closed surfaces exhibiting the highest possible symmetry. We show that if G satisfies certain natural conditions, then all orientable regular embeddings of its canonical double covering, isomorphic to the tensor product G K2 , can be described ...

In this paper, a classification of the regular embeddings of Kn,n, where n = 2e is a power of two, is completed. The number of such regular maps is one or two for e = 1, 2, respectively. For e ≥ 3 there are 2e−2 + 4 regular embeddings of K2e,2e . The method is based on classification of groups G which factorise as a product of two cyclic groups G = XY of order n such that the cyclic factors are...

A family of cliques in a graph G is said to be p-regular if any two cliques in the family intersect in exactly p vertices. A graph G is said to have a p-regular k-clique cover if there is a p-regular family H of k-cliques of G such that each edge of G belongs to a clique in H. Such a p-regular kclique cover is separable if the complete subgraphs of order p that arise as intersections of pairs o...

The total irregularity of a simple undirected graphG is defined as irrt(G) = 1 2 ∑ u,v∈V (G) |dG(u)− dG(v)|, where dG(u) denotes the degree of a vertex u ∈ V (G). Obviously, irrt(G) = 0 if and only if G is regular. Here, we characterize the non-regular graphs with minimal total irregularity and thereby resolve the recent conjecture by Zhu, You and Yang [18] about the lower bound on the minimal ...

It is shown that every abelian regular Lie group is a quotient of its Lie algebra via the exponential mapping. This paper is a sequel of [3], see also [4], chapter VIII, where a regular Lie group is defined as a smooth Lie group modeled on convenient vector spaces such that the right logarithmic derivative has a smooth inverse Evol : C(R, g) → C(R, G), the canonical evolution operator, where g ...

the k-th semi total point graph of a graph g, , ‎is a graph‎ obtained from g by adding k vertices corresponding to each edge and‎ connecting them to the endpoints of edge considered‎. ‎in this paper‎, a formula for laplacian polynomial of in terms of‎ characteristic and laplacian polynomials of g is computed‎, ‎where is a connected regular graph‎.the kirchhoff index of is also computed‎.

let $mathcal{a}$ be a banach algebra with bai and $e$ be an introverted subspace of $mathcal{a'}$.in this paper we study the quotient arens regularity of $mathcal{a}$ with respect to $e$ and prove that the group algebra $l^1(g)$ for a locally compact group $g$, is quotient arens regular with respect to certain introverted subspace $e$ of $l^infty(g)$.some related result are given as well.